Taxi-drivers' representatives expect to meet the Minister with responsibility for their industry, Mr Bobby Molloy, next Tuesday with a view to resolving the crisis.
However, Mr Molloy, Minister of State at the Department of the Environment, stressed last night that the deregulation process was in place and there would be no change to that.
"The process has begun," he said, "and hundreds of applications for taxi plates have been given out."
The leaderships of the three unions or representative bodies will take part in the discussions with Mr Molloy. They are the Irish Taxi-Drivers' Union, SIPTU and the Irish Taxi Drivers' Federation.
Last night, following a meeting between the bodies' executives and Mr Ivor Callely, TD, in Leinster House, the vice-president of the Irish Taxi-Drivers' Union, Mr Vincent Kearns, said Mr Callely would be in contact with Mr Molloy's officials "to set up roundtable talks early next week". A spokesman for Mr Molloy confirmed the meeting was scheduled for Tuesday.
Meanwhile, the Garda arrested a second taxi-driver yesterday over a public order offence at the junction of Kildare Street and St Stephen's Green but otherwise did not engage in any confrontations with the protesters.
The Garda refrained from issuing tickets to taxi-drivers for illegally parking during the protests. Although three Garda tow lorries arrived in Kildare Street yesterday morning they were not used.
The Garda response, according to senior sources, was designed not to inflame the protesters and possibly escalate the disruption.
By last evening the Garda Press Office said only two cars had been towed in any of the protests and during the two days only two arrests were made.
One was for assault on Wednesday and another for the public order offence yesterday. The arrest on Wednesday followed an incident in which a car was driven over a Garda's foot.
The Rehab Group has expressed "deep anger" at comments by some taxi-drivers who said on radio yesterday morning that they opposed the provision of a wheelchair service in their taxis.
One driver told RTE's Morning Ireland programme he felt "very bitter" about the issue of wheelchair accessible taxis.
"Why should I get out on a rainy night, get ramps and push a wheelchair" into the taxi, he said, adding the issue of wheelchair accessible taxis is "the greatest curse ever bestowed on taxidrivers".
Another driver said he normally took seven or eight wheelchair passengers a day, but would not be taking any more until the dispute was resolved.
Mr John Ussher, president of the Irish Taxi-Drivers' Federation, yesterday said the organisation dissociated itself from the comments. A spokeswoman for Rehab said this was not enough. There should be codes of conduct and best practice guidelines in place for taxi-drivers dealing with people with disabilities, she said.
Looking to Tuesday's meeting with Mr Molloy, SIPTU president Mr Des Geraghty said his union would be putting forward the idea of "qualitative deregualtion", which he said would provide a "natural cap" on the number of new taxis coming on-stream.
Shortly after 5 p.m. the majority of taxi vehicles were being moved from Kildare Street and Molesworth Street by their owners. Traffic was moving freely on Kildare Street last night. However rush-hour traffic on and around Pearse Street was brought almost to a halt as taxis which had been removed from the airport were parked in bus lanes.
